# coding: utf-8
#RSA

#随机大素数

import random
import time

# 扩展欧几里的算法
def ext_gcd(a, b):
    if b == 0:
        x1 = 1
        y1 = 0
        x = x1
        y = y1
        r = a
        return r, x, y
    else:
        r, x1, y1 = ext_gcd(b, a % b)
        x = y1
        y = x1 - a // b * y1
        return r, x, y


# 超大整数超大次幂然后对超大的整数取模
def exp_mode(base, exponent, n):
    bin_array = bin(exponent)[2:][::-1]
    r = len(bin_array)
    base_array = []
    
    pre_base = base
    base_array.append(pre_base)
    
    for _ in range(r - 1):
        next_base = (pre_base * pre_base) % n 
        base_array.append(next_base)
        pre_base = next_base
        
    a_w_b = __multi(base_array, bin_array, n)
    return a_w_b % n

def __multi(array, bin_array, n):
    result = 1
    for index in range(len(array)):
        a = array[index]
        if not int(bin_array[index]):
            continue
        result *= a
        result = result % n # 加快连乘的速度
    return result

# Miller-Rabin素性检测算法
def rabin_miller(num):
    s = num - 1
    t = 0
    while s % 2 == 0:
        s = s // 2
        t += 1

    for trials in range(5):
        a = random.randrange(2, num - 1)
        v = exp_mode(a, s, num)
        if v != 1:
            i = 0
            while v != (num - 1):
                if i == t - 1:
                    return False
                else:
                    i = i + 1
                    v = (v ** 2) % num
    return True

def is_prime(num):
    # 排除0,1和负数
    if num < 2:
        return False

    # 创建小素数的列表,可以大幅加快速度
    # 如果是小素数,那么直接返回true
    small_primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]
    if num in small_primes:
        return True

    # 如果大数是这些小素数的倍数,那么就是合数,返回false
    for prime in small_primes:
        if num % prime == 0:
            return False

    # 如果这样没有分辨出来,就一定是大整数,那么就调用rabin算法
    return rabin_miller(num)

# 得到大整数
def get_prime(key_size=1024):
    while True:
        num = random.randrange(2**(key_size-1), 2**key_size)
        if is_prime(num):
            return num

# 生成公钥私钥，p、q为两个超大质数
def gen_key():
    while 1:
        p = get_prime()
        q = get_prime()
        n = p * q
        fy = (p - 1) * (q - 1)      # 计算与n互质的整数个数 欧拉函数
        e = 65537                   # 选取e   一般选取65537
        a = e
        b = fy
        r, x, y = ext_gcd(a, b)     # 需保证x为正数，若x小于0则需要重新生成
        if x>0:
            if exp_mode(exp_mode(1234, x, n), e, n)==1234:  # 模拟加解密，保证密钥是可用的
                break
    d = x
    # 返回：   公钥  私钥
    return      n, d